Analytic Geometry Answers

7.Find the coordinate of the point of interception of the lines: 2x + y = 5 ; x + y = 3
a.(-1,2)
b.(1,2)
c.(1,-1)
d.(2,1)

8.The equation of a straight line at point (2,3) and slope 5 is given by
a.y=5x-3
b.y=5x-10
c.y=5x+3
d.y=3x-5

3.Find the coordinate of the point of interception of the lines: x + 2y = 5 ; x + y = 3
a.(1,2)
b.(−1,2)
c.(1,1)
d.(1,0)

4.Two lines are said to be parallel if
a.their gradient is the same
b.they have equal rate of change
c.the angle between the two lines is zero
d.All the options

1.Let the gradient of a line be 3, find the equation of the line at point(1,2)
a.2y=x
b.y=2x
c.y=x
d.y=3x

2.Find the equation of the line which is parallel to
3x−2y=5 and passes through the point (-2,-4)
a.3x+2y=−5
b.3x+2y=−2
c.(-3x+2y=-2)
d.(3x+2y=6)

A, B, C, D are the points i − k, − i + 2 j, 2i − 3k, 3i − 2 j − k respectively. Show that the
projection of AB on CD is equal to that of CD on AB . Also find the cosine of their
inclination.

A 4kg ball is propelled off a track with a force 200N. The force of gravity on the ball is 40N. Determine the resultant force of the ball.

Write an equation for the circle with centre (0,0) if the point A(6,2) lies on the circle

Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 30° and 120°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

9.Let A, B, C be the points (2,3)(3,−2) and (−1,4)
. The length of AB yields_____
a.square root of 26
b.square root of 27
c.square root of 23
d.square root of 35

10.____ is defined as the ratio of the vertical distance the line rises or falls to the horizontal distance.
a.Gradient of a line
b.Gradient of a helix
c.Gradient of a circle
d.None of the options

7.In Cartesian Coordinates, the coordinates are given by the position
a.of a point in a plane
b.of a point in a circle
c.of a point in a helix
d.of a point in a rhombus

8.The coordinates of the midpoint of a line segment is
a.the average of the coordinates of the endpoints
b.the sum of the coordinates of the endpoints
c.the product of the coordinates of the endpoints
d.None of the options

5.The Locus of points at a distance of 3 from the point (0, 0) is given by the equation…
a.x^2+y^2=−9

b.x^2-y^2=9

c.x^2+y^2=9

d.−x^2+y^2=−9

6.If A is (3, 6) and B is (4, 8). Find the coordinate of the midpoint of AB.
a.[3 1/2,−7]
b.[−3 1/2,7]
c.[−3 1/2,−7]
d.[3 1/2,7]